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A compact ADI scheme for the two dimensional time fractional diffusion‐wave equation in polar coordinates
Author(s) -
Vong Seakweng,
Wang Zhibo
Publication year - 2015
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21976
Subject(s) - mathematics , alternating direction implicit method , polar coordinate system , convergence (economics) , mathematical analysis , stability (learning theory) , partial differential equation , polar , domain (mathematical analysis) , variable (mathematics) , partial derivative , diffusion , diffusion equation , scheme (mathematics) , finite difference , finite difference method , geometry , physics , economy , service (business) , astronomy , machine learning , computer science , economics , economic growth , thermodynamics
In this article, we consider finite difference schemes for two dimensional time fractional diffusion‐wave equations on an annular domain. The problem is formulated in polar coordinates and, therefore, has variable coefficients. A compact alternating direction implicit scheme with O ( τ 3 − α + h 1 4 + h 2 4 ) accuracy order is derived, where τ, h 1 , h 2 are the temporal and spatial step sizes, respectively. The stability and convergence of the proposed scheme are studied using its matrix form by the energy method. Numerical experiments are presented to support the theoretical results. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1692–1712, 2015